We can simplify the position of a point P on a plane by the vector OP where O is a reference point on the plane. The vector OP is called the position vector of P with respect to the reference point O. That is, every point on the plane can be represented by its position vector wrt the reference point O.

Then vector PQ = vector OQ – vector OP.

Furthermore, when we look at the coordinate plane for a point P (x, y), we can use its coordinates x and y to represent its position vector with respect to the origin O. We introduce column vector notation. A column vector is like a special form of a matrix (2 rows, 1 column). All matrix operations apply to column vectors.

We can apply what we have learned about vectors to help us solve geometry problems.

Notice when vector AB = vector DC, it means line AB is parallel to line DC and AB = DC.

While a scalor is a quantity that has only magnitude, a vector is a quantity that has both magnitude and direction. We usually use directed line segment to represent a vector. The direction of the line segment, indicated by an arrow, represents the direction of the vector, and the length of the line segment represents the magnitude of the vector.

Two vectors are equal if they have equal magnitude and are in the same direction.

For vector additions, we study the triangle law and parallelogram law of vector additions.